Apparatus and method for determining state of charge in a redox flow battery via limiting currents

ABSTRACT

The present invention relates to methods and apparatuses for determining the ratio of oxidized and reduced forms of a redox couple in solution, each method comprising: contacting first and second stationary working electrodes and first and second counter electrode to the solution; applying a first potential at the first stationary working electrode and a second potential at the second stationary working electrode relative to the respective counter electrodes and measuring first and second constant currents for the first and second stationary working electrodes, respectively; wherein the first and second constant currents have opposite signs and the ratio of the absolute values of the first and second constant currents reflects the ratio of the oxidized and reduced forms of the redox couple in solution. When used in the context of monitoring/controlling electrochemical cells, additional embodiments include those further comprising oxidizing or reducing the solution.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a divisional of U.S. patent application Ser. No.15/033,607, filed Apr. 29, 2016, that is a 35 U.S.C. § 371 NationalStage Entry of International Patent Application PCT/US2014/063290, filedon Oct. 31, 2014, which claims the benefit of priority to U.S.Provisional Patent Application Ser. No. 61/898,635, filed on Nov. 1,2013, the contents of each of which is incorporated by reference in itsentirety for any and all purposes.

TECHNICAL FIELD

The present invention relates to redox flow batteries and methods andapparatuses for monitoring the compositions of the electrolytes therein.

BACKGROUND

Flow batteries are electrochemical energy storage systems in whichelectrochemical reactants, typically redox active compounds, aredissolved in liquid electrolytes, which are individually contained innegolyte and posolyte loops and circulated through reaction cells whereelectrical energy is either converted to or extracted from chemicalpotential energy in the reactants by way of reduction and oxidationreactions. Especially in larger systems, which may comprise multipleelectrochemical cells or stacks, it is important to be able to monitorthe state-of-charge of each of the electrolytes, for example to knowwhen the flow battery is “full” or “empty” before actually realizingthese end states.

Additionally, for optimal performance, the initial state of such asystem provides that the negolyte and posolyte contain equimolarquantities of the redox active species and that the negolyte state ofcharge and posolyte state of charge are equivalent. But after the systemhas experienced some number of charge/discharge cycles, the posolyte andnegolyte may become imbalanced because of side reactions during theseoperations—for example, generation of hydrogen or oxygen from water ifoverpotential conditions are breached—causing the imbalance andassociated loss of performance.

An imbalanced state may be corrected by processing the electrolyte in arebalancing cell. But before this can be done, it is necessary to assessthe state of charge of the system and often the individual electrolytes.State of charge for flow batteries is a way of expressing the ratio ofconcentrations of charged to uncharged active material. State of chargemonitoring for flow battery electrolyte has typically been done usingspectroscopic methods or by potential measurements. Spectroscopicmeasurements typically rely on well-established spectroscopic methods,most often relying on a color change and measurement by UV-Visiblespectroscopy. Electrochemical measurements are a more direct way toestablish state of charge. Most of these methods are based on measuringthe potential of the electrolyte solution, which may be related to theconcentration ratio through the Nernst equation. Such potentialmeasurements require a reference electrode which can be prone topotential drift and ‘fouling’ when in contact with electrolyte forextended periods, making it difficult to obtain the absolute potentialof the solution relative to a defined standard. For certain electrolytecompositions the relationship between state-of-charge and potential maynot be accurately described by the Nernst equation.

The present invention addresses some of these deficiencies.

SUMMARY

Certain embodiments provide methods of determining the ratio of oxidizedand reduced forms of a redox couple in solution, each method comprising:

-   -   (a) contacting a first stationary working electrode and a first        counter electrode to the solution;    -   (b) applying a first potential at the first working electrode        and measuring a first constant current;    -   (c) applying a second potential at the first working electrode        and measuring a second constant current;    -   wherein the sign of the first and second currents are not the        same; and    -   wherein the ratio of the absolute values of the first and second        currents reflects the ratio of the oxidized and reduced forms of        the redox couple in solution. When used in the context of        monitoring/controlling electrochemical cells, stacks, or        systems, additional embodiments include those further        comprising (d) oxidizing or reducing the solution, so as to        alter the balance of the oxidized and reduced forms of the redox        couple in solution, to a degree dependent on the ratio of the        absolute values of the first and second currents.

In other embodiments, it is also possible to use two pairs ofelectrodes, operating in tandem to the same effect as the single pairconfiguration. Accordingly, additional embodiments provide methods ofdetermining the ratio of the oxidized and reduced forms of a redoxcouple in solution, each method comprising:

-   -   (a) contacting a first stationary working electrode and a first        counter electrode to the solution;    -   (b) contacting a second stationary working electrode and a        second counter electrode to the solution;    -   (c) applying a first potential at the first working electrode        relative to the first counter electrode and measuring a first        constant current for the first working electrode;    -   (d) applying a second potential at the second working electrode        relative to the second counter electrode and measuring a second        constant current for the second working electrode;    -   wherein the first and second currents have opposite signs; and    -   wherein the ratio of the absolute values of the first and second        currents reflects the ratio of the oxidized and reduced forms of        the redox couple in solution. When used in the context of        monitoring/controlling electrochemical cells, additional        embodiments further comprises (e) oxidizing or reducing the        solution, so as to alter the balance of the oxidized and reduced        forms of the redox couple in solution, to a degree dependent on        the ratio of the absolute values of the first and second        currents.

The invention also teaches energy storage systems, each systemcomprising:

(a) a fluidic loop containing a first electrolyte solution and aseparate fluidic loop containing a second electrolyte solution;

(b) at least one pair of electrodes each independently in fluidiccontact with the first electrolyte solution or each of the first andsecond electrolyte solutions, each pair of electrodes consisting of afirst stationary working electrode and a first counter electrode; and

(c) an optional control system, including a power source and sensors,associated with each pair of electrodes, said control system configuredto be capable of applying first and second electric potentials at eachof the first working electrodes relative to the first counterelectrodes, and measuring the first and second currents associated withsaid electric potential; and

(d) optional software capable of calculating the ratio of the absolutevalues of the first and second currents between each electrode pairs,which reflects the ratio of the oxidized and reduced forms of the redoxcouple in solution. Such energy systems may further comprise at leastone rebalancing sub-system associated with each electrode pair.

BRIEF DESCRIPTION OF THE DRAWINGS

The present application is further understood when read in conjunctionwith the appended drawings. For the purpose of illustrating the subjectmatter, there are shown in the drawings exemplary embodiments of thesubject matter; however, the presently disclosed subject matter is notlimited to the specific methods, devices, and systems disclosed. Inaddition, the drawings are not necessarily drawn to scale. In thedrawings:

FIG. 1 provides a schematic representation of a redox flow batteryincorporating a state of charge measurement apparatus.

FIG. 2 describes one electrode configuration described herein.

FIG. 3 shows the relationship of current as a function of time for theoxidation and reduction of 1 M iron hexacyanide at 20 mol % Fe³⁺/80 mol% Fe²⁺ using glassy carbon electrodes, as described in Example 1.

FIG. 4 shows the relationship of current as a function of time for theoxidation and reduction of 1 M iron hexacyanide at 60 mol % Fe³⁺/40 mol% Fe²⁺ using glassy carbon electrodes, as described in Example 1.

FIG. 5 shows the relationship of current as a function of time for theoxidation and reduction of 1 M iron hexacyanide at 95 mol % Fe³⁺/5 mol %Fe²⁺ using glassy carbon electrodes, as described in Example 1.

FIG. 6 shows the relationship of current as a function of time for theoxidation and reduction of 0.92 M iron hexacyanide at 36 mol % Fe³⁺/64mol % Fe²⁺ using glassy carbon electrodes, as described in Example 2.

FIG. 7 shows the relationship of current as a function of time for theoxidation and reduction of 0.92 M iron hexacyanide at 53.4 mol %Fe³⁺/46.6 mol % Fe²⁺ using glassy carbon electrodes, as described inExample 2.

FIG. 8 shows the relationship of current as a function of time for theoxidation and reduction of 0.92 M iron hexacyanide at 76.8 mol %Fe³⁺/23.2 mol % Fe²⁺ using glassy carbon electrodes, as described inExample 2.

FIG. 9 shows the relationship of current as a function of time for theoxidation and reduction of 0.92 M iron hexacyanide at 100 mol % Fe³⁺/0mol % Fe²⁺ using glassy carbon electrodes, as described in Example 2.

DETAILED DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS

The present invention relates to redox flow batteries and methods andapparatuses for monitoring the compositions of the electrolytes(posolyte or negolyte or both) therein. In particular, the presentinvention relates to methods and configurations whose use consistsessentially of a first stationary working electrode and a first counterelectrode (or two pairs of working and counter electrodes) to measurethe ratio of oxidized and reduced forms of a redox couple, and so thestate of charge of an electrolyte. The methods of this invention arebased on the use of limiting current between a set of electrodes and donot rely on a reference electrode to measure or control potential. Whenused as part of a control and monitoring system for a redox flow battery(or other electrochemical device) as feedback for charge and dischargecycles and an indicator in any state of charge loss or imbalance thatmay occur during operation, this invention thereby allows the adjustmentof the ratio or state-of-charge for optimal performance of theelectrochemical device.

The present invention may be understood more readily by reference to thefollowing description taken in connection with the accompanying Figuresand Examples, all of which form a part of this disclosure. It is to beunderstood that this invention is not limited to the specific products,methods, conditions or parameters described and/or shown herein, andthat the terminology used herein is for the purpose of describingparticular embodiments by way of example only and is not intended to belimiting of any claimed invention. Similarly, unless specificallyotherwise stated, any description as to a possible mechanism or mode ofaction or reason for improvement is meant to be illustrative only, andthe invention herein is not to be constrained by the correctness orincorrectness of any such suggested mechanism or mode of action orreason for improvement. Throughout this text, it is recognized that thedescriptions refer to compositions and methods of making and using saidcompositions. That is, where the disclosure describes and/or claims afeature or embodiment associated with a system or apparatus or a methodof making or using a system or apparatus, it is appreciated that such adescription and/or claim is intended to extend these features orembodiment to embodiments in each of these contexts (i.e., system,apparatus, and methods of using).

In the present disclosure the singular forms “a,” “an,” and “the”include the plural reference, and reference to a particular numericalvalue includes at least that particular value, unless the contextclearly indicates otherwise. Thus, for example, a reference to “amaterial” is a reference to at least one of such materials andequivalents thereof known to those skilled in the art, and so forth.

When a value is expressed as an approximation by use of the descriptor“about,” it will be understood that the particular value forms anotherembodiment. In general, use of the term “about” indicates approximationsthat can vary depending on the desired properties sought to be obtainedby the disclosed subject matter and is to be interpreted in the specificcontext in which it is used, based on its function. The person skilledin the art will be able to interpret this as a matter of routine. Insome cases, the number of significant figures used for a particularvalue may be one non-limiting method of determining the extent of theword “about.” In other cases, the gradations used in a series of valuesmay be used to determine the intended range available to the term“about” for each value. Where present, all ranges are inclusive andcombinable. That is, references to values stated in ranges include everyvalue within that range.

It is to be appreciated that certain features of the invention whichare, for clarity, described herein in the context of separateembodiments, may also be provided in combination in a single embodiment.That is, unless obviously incompatible or specifically excluded, eachindividual embodiment is deemed to be combinable with any otherembodiment(s) and such a combination is considered to be anotherembodiment. Conversely, various features of the invention that are, forbrevity, described in the context of a single embodiment, may also beprovided separately or in any sub-combination. Finally, while anembodiment may be described as part of a series of steps or part of amore general structure, each said step may also be considered anindependent embodiment in itself, combinable with others.

When a list is presented, unless stated otherwise, it is to beunderstood that each individual element of that list, and everycombination of that list, is a separate embodiment. For example, a listof embodiments presented as “A, B, or C” is to be interpreted asincluding the embodiments, “A,” “B,” “C,” “A or B,” “A or C,” “B or C,”or “A, B, or C.”

The following descriptions are believed to be helpful in understandingthe present invention(s). Starting from first principles, an electrolytein a flow battery consists of an active material which can storeelectrons; the active material thus exists in both a charged state and adischarged (or uncharged) state. If all the active material isdischarged the electrolyte is said to have a state of charge of 0%,conversely, if all the active material is in the charged state the stateof charge is 100%. At any intermediate state of charge (0%<SOC<100%)there will be a non-zero concentration of both charged active materialand discharged active material. When current is passed through anelectrode in contact with such an electrolyte molecules of the activematerial will either charge or discharge depending on the potential ofthe electrode. For an electrode of finite area the limiting currentdensity (i_(limiting)) will be proportional to the concentration of thespecies being consumed by the electrochemical process.

For example if an active material at 50% SOC has an equilibriumpotential of 0 V, and an electrode is held at +100 mV, discharged activematerial will be converted to charged active material and a current forthis oxidation can be measured at the electrode. Assuming the volume andconcentration of the active material is large the SOC will not changesignificantly, and the current will approach a constant value after thevoltage has been held for a short time. This limiting current density(him, current per unit electrode surface area) depends on the bulkconcentration (C) of the discharged active material (the species beingdepleted), the diffusion coefficient (D) of the discharged activematerial, the thickness of the diffusion layer (δ), and the number ofelectrons (n) transferred in the reaction according to the followingequation:

$i_{\lim} = {\frac{n\; {FD}}{\delta}C}$

Thus if the diffusion coefficient and diffusion layer thickness areknown the concentration of charged active material or discharged activematerial can be directly determined by measuring the limiting currentduring oxidative or reductive traversal of the electrochemical couple.In practice precise determination of D and δ are non-trivial, so thisinvention will rely only on determining the concentration ratio of thecharged active material to discharged active material by measuring theratio of limiting currents for the oxidative and reductive process.

For a reversible electrochemical couple there is minimal structural orchemical change between the charged and discharged molecular species(for quasi-reversible or less reversible electrochemical couples, thesame principles are in play, albeit with increasing associated errors.In some applications, these increasing errors may be acceptable orcorrectable, so as to allow the present methods to be used with thesesystems as well). This means that for the oxidative process (ox) andreductive process (red), the diffusion coefficients and diffusion layerthickness will be similar for both processes, i.e. D_(ox)≈D_(red) andδ_(ox)≈δ_(red). Faraday's constant and the number of electrons will beunchanged such that:

$\frac{i_{\lim,{ox}}}{i_{\lim,{red}}} \propto {A\; \frac{C_{red}}{C_{ox}}}$

where A can either be unity (in the ideal case) or a correction constantto account for differences in the diffusion coefficient or diffusionlayer as determined experimentally by other methods. C_(ox) is theconcentration of the oxidized form of the active material (depleted uponreduction), and C_(red) is the concentration of the reduced form of theactive material (depleted upon oxidation). The ratio of concentrations(or limiting currents) can be easily converted to SOC as a percentage:

${SOC} = {{100\frac{\frac{C_{ox}}{C_{red}}}{1 + \frac{C_{ox}}{C_{red}}}} = {100\; \frac{A\; \frac{i_{\lim,{red}}}{i_{\lim,{ox}}}}{1 + {A\; \frac{i_{\lim,{red}}}{i_{\lim,{ox}}}}}}}$

Despite the apparent simplicity of this approach, it does not appearthat these relationships have been recognized or applied by thoseskilled in the art of electrochemistry to flow battery systems.

In practice, the above equations represent an ideal case, and the ratioof currents may need to be related to the state of charge in a moreempirical fashion. In the case of using multiple sets of electrodes thesurface areas of the working electrodes may be selected such that theyare not equivalent, in which case the ratio of currents and the ratio ofcurrent densities would be inequivalent (I_(ox)/I_(red)≠i_(ox)/i_(red)).Additionally the diffusion coefficients and diffusion layer thicknessesfor the oxidized and reduced species, though similar, will not beequivalent. In some embodiments the potential holds chosen may be suchthat the difference between the oxidative hold and E_(1/2) and thedifference between the reductive hold and E_(1/2) are not the samemagnitude, such that even with no change in diffusion characteristics(D_(ox)=D_(red) and δ_(ox)=δ_(ox)) the proportionality constant A may besignificantly different from unity.

These factors can be accounted for by calibrating the limiting currenttechnique across the state of charge range. For example the oxidativeand reductive currents for a particular mode of operation (surfaceareas, potential magnitudes, etc.) would be measured at multiple SOC's.The state of charge could be independently measured by another techniquesuch as spectroscopy or charge counting. The current ratioI_(ox)/I_(red) could then be related to C_(ox)/C_(red) determined fromthe independent method via a proportionality constant (i.e. A in theabove equations) or by a more complex formula. AlternativelyI_(ox)/I_(red) could be immediately converted to a ‘raw’ SOC by makingno such correction, but then subsequently the ‘raw’ SOC could be relatedto the independently measured SOC to give the appropriate correctionfactor or formula.

The limiting current for either the oxidative or reductive process canbe measured by a simple three electrode experiment (working, counter,and reference). For example if the E_(1/2) for an electrolyte couple is0 V vs. Ag⁺/Ag⁰ the working electrode could be held at +100 mV vs.Ag⁺/Ag⁰, and the current measured vs. time. After a short time thecurrent would reach a near constant value which would establish thelimiting oxidative current I_(lim,ox). Repeating the experiment at −100mV vs. Ag⁺/Ag⁰ would establish the limiting reductive currentI_(lim,red). If the same electrode were used in each experiment thesurface area would be the same and the current ratio would be equivalentto the current density ratio from which the concentration ratio could bedetermined.

However, a reference electrode is not required to obtain similarinformation. When a third reference electrode is not employed, the firstand second potentials at the first working electrode are generallyapplied relative to the first counter electrode; the potential is heldrelative to the solution potential measured at the counter electrode. Inthis scenario any electrolyte couple has a potential of 0 V vs. solutionpotential, and the working electrode can be held at either positive ornegative potential vs. that solution potential (e.g., +100 mV for theoxidation, or −100 mV for the reduction). Again the limiting current canbe measured once it becomes constant or near constant.

With this background, it is possible to enumerate the many embodimentsof the present invention.

Certain embodiments provide methods of determining the ratio of oxidizedand reduced forms of a redox couple in solution, each method comprising:

-   -   (d) contacting a first stationary working electrode and a first        counter electrode to the solution;    -   (e) applying a first potential at the first working electrode        and measuring a first constant current;    -   (f) applying a second potential at the first working electrode        and measuring a second constant current;

wherein the sign of the first and second currents are not the same; and

wherein the ratio of the absolute values of the first and secondcurrents reflects the ratio of the oxidized and reduced forms of theredox couple in solution, according to the equations described above.This ratio may be used simply to monitor an electrochemical cell eitherat various intervals or in real-time, so as to know when to adjust thecurrent inputs or outputs from said system. Alternatively, when suchmethods are individually applied to both of the posolyte and negolyte ofan electrochemical, a comparison of the ratios may be used as a basisfor determining the need for rebalancing either or both of theelectrolytes. For example, additional embodiments include thosecomprising the steps already described in this paragraph, and furthercomprising (d) oxidizing or reducing the solution, so as to alter thebalance of the oxidized and reduced forms of the redox couple insolution, to a degree dependent on the ratio of the absolute values ofthe first and second currents. These embodiments may be used in thecontext of maintaining an electrochemical cell, stack, or system.

Whether described as methods of determining the ratio of oxidized andreduced forms of a redox couple in solution or methods of maintaining anelectrochemical cell, stack, or system, in certain of these methodsemploying a first stationary working electrode and a first counterelectrode, the methods may be conducted in the absence or presence of athird (reference) electrode. That is, use of a reference or thirdelectrode is not necessarily required.

The methods may be conducted such that the first potential is morepositive than the equilibrium potential of the redox couple; and thesecond potential is more negative than the equilibrium potential of theredox couple. In other sometimes overlapping embodiments, the magnitudeof the difference between the first potential and the equilibriumpotential and the magnitude of the difference between the equilibriumpotential and the second potential are substantially the same. Thesemethods may be done such that the first and second potentials may be,but are not necessarily, of substantially the same magnitude butopposite in sign. As used herein in the context of potentialdifferences, the term “substantially the same” is intended to connote adifference of less than about 20%, relative to the mean of the twovalues. In practice, the user will likely seek to achieve near parity ofmagnitudes, as much as practicably possible, but additional provide thatthis difference is less than 25%, 15%, 10%, or 5%, relative to the meanvalue of the two potentials.

The working and counter electrodes are typically, but not necessarily,differently sized, for example, such that the first working and counterelectrodes each has a surface area contacting the solution, and thesurface area of the working electrode is less than that of the counterelectrode. Such an arrangement encourages the limiting of the current tobe at the working electrode. Without being bound by the correctness orincorrectness of any particular theory, it is believed that if thecounter electrode becomes smaller (relative to the working electrode)the current will then be limited at the counter and not the workingelectrode, the sign of the currents will still be set by the sign of thepotential, but the magnitude will now be controlled by reactions at thecounter which is the opposite direction of the reaction occurring at theworking electrode. The calculations may be adjusted for this difference,so long as it is appreciated (i.e., in such circumstances, the roles ofthe working and counter electrodes have been reversed). Using a largersize ratio avoids any confusion or contribution of effects at bothelectrodes. In certain preferred embodiments, the surface area of thefirst working electrode is less than about 20%, more preferably in arange of about 1% to 10%, of that of the first counter electrode,through additional embodiments provide that the surface area of thefirst working electrode may be from about 5%, 10%, 20%, 30%, 40%, or 50%to about 90%, 80%, 70%, 60%, or 50% of the first counter electrode.

In other embodiments, it is also possible to use two pairs ofelectrodes, operating in tandem to the same effect as the single pairconfiguration. That is, certain embodiments provide methods ofdetermining the ratio of the oxidized and reduced forms of a redoxcouple in solution, each method comprising:

-   -   (a) contacting a first stationary working electrode and a first        counter electrode to the solution;    -   (b) contacting a second stationary working electrode and a        second counter electrode to the solution;    -   (c) applying a first potential at the first working electrode        relative to the first counter electrode and measuring a first        constant current for the first working electrode;    -   (d) applying a second potential at the second working electrode        relative to the second counter electrode and measuring a second        constant current for the second working electrode;

wherein the first and second currents have opposite signs; and

wherein the ratio of the absolute values of the first and secondcurrents reflects the ratio of the oxidized and reduced forms of theredox couple in solution. Analogous to the single electrode pairarrangement, this ratio may be used simply to monitor an electrochemicalcell either at various intervals or in real-time, so as to know when toadjust the current inputs or outputs from said system. Alternatively,when such methods are individually applied to both of the posolytes andnegolytes of an electrochemical, a comparison of the ratios may be usedas a basis for determining the need for rebalancing either or both ofthe electrolytes. For example, additional embodiments include thosecomprising the steps already described in this paragraph, and furthercomprising (e) oxidizing or reducing the solution, so as to alter thebalance of the oxidized and reduced forms of the redox couple insolution, to a degree dependent on the ratio of the absolute values ofthe first and second currents. These embodiments may be also be used inthe context of maintaining an electrochemical cell, stack, or system. Inthe case of these twin pair electrode arrangements, the first and secondpotentials are applied at each electrode pair at the same time(simultaneously) or at staggered times.

Whether described as methods of determining the ratio of oxidized andreduced forms of a redox couple in solution or methods of maintaining anelectrochemical cell, stack, or system, in certain of these methodsemploying twin pairs of stationary working electrodes and counterelectrodes, the methods may be conducted in the absence or presence ofthird (reference) electrodes. That is, use of a reference or thirdelectrode is not necessarily required. When a third reference electrodeis not employed, the first and second potentials at the first workingelectrode are generally applied relative to the respective counterelectrode.

The terms “twin pairs” or “matched pairs” of stationary workingelectrodes and counter electrodes is not intended to connote that therespective electrodes are necessarily of identical or complementarysizes, or that the first working electrode only works with the firstcounter electrode and that the second working electrode only works withthe second counter electrode, though in fact either of these conditionsmay be true. Rather, the terms are intended to connote that two sets ofsimilarly sized electrodes are present and used, alternatively if setsof differently sized electrodes are used this difference may need to beappreciated and adjusted for in calculation. However, in preferredembodiments where so-called twin pairs of electrodes are used, theworking and counter electrode of each pair are positioned to bespatially close to one another, while each pair are positioned to bespatially separated to prevent cross currents. One pair would bepolarized to a positive potential to measure the oxidative limitingcurrent, and one pair would be polarized negatively to measure thereductive limiting current.

Such a device would hold each pair of electrodes at the appropriatepotentials and measure the current through each loop. The ratio of thelimiting currents can be directly displayed or recorded and will beequivalent, or practically equivalent provided equal or near equalworking electrode surface areas, to the ratio of the limiting/constantcurrent densities and equivalent (or proportional) to the concentrationratio. Concerns about the electrode surface area changing over time canbe alleviated by periodically switching which pair was measuring thereductive process and which the oxidative process, such that any changein surface area (as a result of electrode fouling) would occur evenly onboth electrodes. The invention also extends to a device capable ofacting as a simple potentiostat to hold each pair of electrodes atconstant potential and measure the resulting current, and a simplealgorithm to compute the ratio of the currents and convert it toconcentrations or states of charge based on other user inputs.

In certain embodiments, where the first and second working electrodesand the first and second counter electrodes each have a surfacecontacting the solution, each of the first and second working electrodesurface areas may be less than the respective or individual areas of thefirst and second counter electrodes, such that the current response isbe determined only or predominantly by limiting (constant) currentdensities of the working electrodes. In other embodiments, sometimesoverlapping, each surface area of the first and second workingelectrodes is substantially the same and each of the first and secondcounter electrodes is substantially the same. The term “substantiallythe same” in this context refers to areas within about 10% of oneanother. In practice, one would probably just use two similarly sized(e.g., same model number) working electrodes as manufactured. Assignificant variances in size would provide for a significant source oferror, the skilled artisan would likely look for electrodes in which thedifference in areas to be close to or within the manufacturer'sspecification for the stated area of the electrode.

As in the single electrode pair arrangement, the relative surface areasof the working and counter electrodes may be configured such that, incertain preferred embodiments the surface areas of the first and secondworking electrodes are each less than about 20%, more preferably in arange of about 1% to about 10%, of the surface areas of the first andsecond counter electrodes, respectively, through additional embodimentsprovide that the surface area of the working electrodes may be fromabout 5%, 10%, 20%, 30%, 40%, or 50% to about 90%, 80%, 70%, 60%, or 50%of the respective counter electrodes.

As with the single pair systems, the methods employing twin pairs ofelectrodes may be conducted such that the first potential is morepositive than the equilibrium potential of the redox couple; and thesecond potential is more negative than the equilibrium potential of theredox couple. In other embodiments, sometimes overlapping, the magnitudeof the difference between the first potential and the equilibriumpotential and the magnitude of the difference between the equilibriumpotential and the second potential are substantially the same. Thesemethods may be done such that the first and second potentials may be,but are not necessarily, of substantially the same magnitude butopposite in sign.

Whether using one or two pair electrode systems, additional individualembodiments provide that the ratio of the oxidized and reduced forms ofthe redox couple are in a range of from about 1:99, 5:95, 10:90, 15:85,20:80, 25:75, 30:70, 35:65, 40:60, 45:55, 50:50, 55:45, 60:40, 65:35,70:30, 75:25, 80:20, 85:15, 90:10, 95:5, or about 99:1. In preferredembodiments, the ratio of the oxidized and reduced forms of the redoxcouple are in a range of from about 20:80 to about 80:20.

The methods are flexible in their utility with a range of redox couplesand electrolytes, including those couples comprising a metal ormetalloid of Groups 2-16, including the lanthanide and actinideelements; for example, including those where the redox couple comprisesAl, As, Ca, Ce, Co, Cr, Cu, Fe, Mg, Mn, Mo, Ni, Sb, Se, Si, Sn, Ti, V,W, Zn, or Zr, including coordination compounds of the same, and eitherwith aqueous or non-aqueous electrolyte solutions. Additionally, themethods are useful in flowing or static electrolytes. In such cases, itis highly preferred that the voltages applied are appropriate or thelocal flow around the working electrode(s) is low enough to allow thelimiting current to be reached.

For reasons described above, the methods are particularly suited for usewith reversible redox couples but may also be used with quasi-reversiblecouples.

Additionally, the methods are flexible in their choice of electrodematerials, though in certain preferred embodiments, at least one of theworking electrodes or counter electrodes comprises an allotrope ofcarbon, including doped forms of carbon, more preferably comprisinggraphite or diamond.

The methods have been described thus far in terms of first and secondconstant currents. This constant current can be calculated from analysisof a current vs. time plot. In preferred embodiments, reference to“constant currents” refer to stable, limiting currents which establishafter extended application (e.g., one minute) of the respective firstand second potentials. However, for the sake of clarity, the constancyof at least one of the first or second current may also be characterizedas exhibiting a change of less than 0.1% over one second or by a changeof less than 1% over ten seconds. In other embodiments, constancy ofcurrent may also refer to less than 5%, 2%, 1%, 0.5%, or 0.1% overperiods of 1, 2, 5, 10, 20, or 60 seconds. Obviously, lesser changesover longer times are more likely to reflect more stable and usefulresults

Because these methods are useful in any application where it is notnecessary to quantify individual oxidized and reduced forms of a redoxcouple, for example where the absolute concentration of the couple isfixed and only the ratio of the forms is changing, the methods areparticularly suited for use in flow battery systems, wherein thesolution is contained within a half-cell fluidic loop of an operatingelectrochemical cell (for example an operating flow battery cell orloop), said operating electrochemical cell generating or storingelectrical energy. In those methods described above as comprisingoxidizing or reducing the solution, so as to alter the balance of theoxidized and reduced forms of the redox couple in solution, to a degreedependent on the ratio of the absolute values of the first and secondcurrents, additional embodiments provide that this be doneelectrochemically. In other embodiments, this may be accomplished by theaddition of chemical oxidizing or reducing agents. Where doneelectrochemically, the oxidizing or reducing of the solution may be donein a rebalancing sub-system, for example, in cases where the state ofcharge of the negolyte and state of charge of the posolyte weredifferent from one another or from the desired state. In otherembodiments, for driving the storage or retrieval of energy, the stateof charge monitor can be used as the control for rate, step times,stopping times, and other operational features, in which case theelectrochemical method may be done by the main flow battery cell, stack,or system.

To this point, the invention has been described in terms of methods ofdetermining the ratio of oxidized and reduced forms of a redox couple insolution or methods of maintaining the balance in electrochemicalsystems, but it should be appreciated that other embodiments includethose systems and associated characteristics useful in employing thesemethods. That is, certain other embodiments provide energy storagesystems, each system comprising:

(a) a fluidic loop containing a first electrolyte solution and aseparate fluidic loop containing a second electrolyte solution; and

(b) at least one pair of electrodes each independently in fluidiccontact with the first electrolyte solution or each of the first andsecond electrolyte solutions, each pair of electrodes consisting of afirst stationary working electrode and a first counter electrode. Theseelectrolyte solutions and electrodes may comprise any of thecharacteristics and configurations described above for the methods.

Other embodiments provide that the energy storage system furthercomprises (c) a control system, including a power source and sensors,associated with each pair of electrodes, said control system configuredto be capable of applying first and second electric potentials at eachof the first working electrodes relative to the first counterelectrodes, and measuring the first and second currents associated withsaid electric potential.

Still further embodiments provide that the energy storage system stillfurther comprises: (d) software capable of calculating the ratio of theabsolute values of the first and second currents between each electrodepairs, which reflects the ratio of the oxidized and reduced forms of theredox couple in solution.

In additional embodiments, the energy storage system even furthercomprises at least one rebalancing sub-system associated with eachelectrode pair, said rebalancing system in fluid communication with thefirst electrolyte loop or with each of the first and second electrolyteloops, said rebalancing sub-system controllable by the control system tooxidize or reduce the electrolyte solution(s) in the respectiverebalancing sub-system in response to the calculated ratio of theabsolute values of the first and second currents between each electrodepairs.

In any one of these embodiments, the first electrolyte solution may be aposolyte solution and the second electrolyte solution may be a negolytesolution. In other embodiments, the nature of the electrolytes isreversed, such that the first electrolyte solution is a negolytesolution and the second electrolyte solution is a posolyte solution.

More broadly, the device is not limited to energy storage/releasingsystems, and certain embodiments provide for devices, each devicecomprising:

(a) at least one pair of electrodes that can each independently be influidic contact with an electrolyte solution, each pair of electrodesconsisting of a first stationary working electrode and a first counterelectrode; and

(b) a control system, including a power source and sensors, associatedwith each pair of electrodes, said control system configured to becapable of applying first and second electric potentials at each of thefirst working electrodes relative to the first counter electrodes, andmeasuring the first and second currents associated with said electricpotential; and

(c) software capable of calculating the ratio of the absolute values ofthe first and second currents between each electrode pairs, whichreflects the ratio of the oxidized and reduced forms of the redox couplein solution.

Terms

Throughout this specification, words are to be afforded their normalmeaning, as would be understood by those skilled in the relevant art.However, so as to avoid misunderstanding, the meanings of certain termswill be specifically defined or clarified.

As used herein, the term “redox couple” is a term of the art generallyrecognized by the skilled electrochemist and refers to the oxidized(electron acceptor) and the reduced (electron donor) forms of thespecies of a given redox reaction. The pair Fe(CN)₆ ³⁺/Fe(CN)₆ ⁴⁺ is butone, non-limiting, example of a redox couple. Similarly, the term “redoxactive metal ion” is intended to connote that the metal undergoes achange in oxidation state under the conditions of use. As used herein,the term “redox couple” may refer to pairs of organic or inorganicmaterials. As described herein, inorganic materials may include “metalligand coordination compounds” or simply “coordination compounds” whichare also known to those skilled in the art of electrochemistry andinorganic chemistry. A (metal ligand) coordination compound may comprisea metal ion bonded to an atom, molecule, or ion. The bonded atom ormolecule is referred to as a “ligand”. In certain non-limitingembodiments, the ligand may comprise a molecule comprising C, H, N,and/or O atoms. In other words, the ligand may comprise an organicmolecule or ion. In some embodiments of the present inventions, thecoordination compounds comprise at least one ligand that is not water,hydroxide, or a halide (F⁻, Cl⁻, Br⁻, I⁻), though the invention is notlimited to these embodiments. Additional embodiments include those metalligand coordination compounds described in U.S. patent application Ser.No. 13/948,497, filed Jul. 23, 2013, which is incorporated by referenceherein in its entirety at least for its teaching of coordinationcompounds.

Unless otherwise specified, the term “aqueous” refers to a solventsystem comprising at least about 98% by weight of water, relative tototal weight of the solvent. In some applications, soluble, miscible, orpartially miscible (emulsified with surfactants or otherwise)co-solvents may also be usefully present which, for example, extend therange of water's liquidity (e.g., alcohols/glycols). When specified,additional independent embodiments include those where the “aqueous”solvent system comprises at least about 55 wt %, at least about 60 wt %,at least about 70 wt %, at least about 75 wt %, at least about 80%, atleast about 85 wt %, at least about 90 wt %, at least about 95 wt %, orat least about 98 wt % water, relative to the total solvent. It somesituations, the aqueous solvent may consist essentially of water, and besubstantially free or entirely free of co-solvents or other species. Thesolvent system may be at least about 90 wt %, at least about 95 wt %, orat least about 98 wt % water, and, in some embodiments, be free ofco-solvents or other species. Unless otherwise specified, the term“non-aqueous” refers to a solvent system comprising less than 10% byweight of water, generally comprising at least one organic solvent.Additional independent embodiments include those where the “non-aqueous”solvent system comprises less than 50 wt %, less than 40 wt %, less than30 wt %, less than 20 wt %, less than 10%, less than 5 wt %, or lessthan 2 wt % water, relative to the total solvent.

In addition to the redox active materials, an aqueous electrolyte maycontain additional buffering agents, supporting electrolytes, viscositymodifiers, wetting agents, and the like.

As used herein, the terms “negative electrode” and “positive electrode”are electrodes defined with respect to one another, such that thenegative electrode operates or is designed or intended to operate at apotential more negative than the positive electrode (and vice versa),independent of the actual potentials at which they operate, in bothcharging and discharging cycles. The negative electrode may or may notactually operate or be designed or intended to operate at a negativepotential relative to the reversible hydrogen electrode. The negativeelectrode is associated with the first aqueous electrolyte and thepositive electrode is associated with the second electrolyte, asdescribed herein.

The terms “negolyte” and “posolyte,” as used herein, refer to theelectrolytes associated with the negative electrode and positiveelectrodes, respectively.

As used herein, unless otherwise specified, the term “substantiallyreversible couples” refers to those redox pairs wherein the voltagedifference between the anodic and cathodic peaks is less than about 0.3V, as measured by cyclic voltammetry, using an ex-situ apparatuscomprising a flat glassy carbon disc electrode and recording at 100mV/s. However, additional embodiments provide that this term may alsorefer to those redox pairs wherein the voltage difference between theanodic and cathodic peaks is less than about 0.2 V, less than about 0.1V, less than about 0.075 V, or less than about 0.059 V, under these sametesting conditions. The term “quasi-reversible couple” refers to a redoxpair where the corresponding voltage difference between the anodic andcathodic peaks is in a range of from 0.3 V to about 1 V.

The term “stack” or “cell stack” or “electrochemical cell stack” refersto a collection of individual electrochemical cells that areelectrically connected. The cells may be electrically connected inseries or in parallel. The cells may or may not be fluidly connected.

The term “state of charge” (SOC) is well understood by those skilled inthe art of electrochemistry, energy storage, and batteries. The SOC isdetermined from the concentration ratio of reduced to oxidized speciesat an electrode (X_(red)/X_(ox)) by the equation:

${SOC} = {{100\; \frac{\frac{C_{ox}}{C_{red}}}{1 + \frac{C_{ox}}{C_{red}}}} = {100\; \frac{A\; \frac{i_{\lim,{red}}}{i_{\lim,{ox}}}}{1 + {A\frac{\; i_{\lim,{red}}}{i_{\lim,{ox}}}}}}}$

where A=1 in ideal cases. For example, in the case of an individualhalf-cell, when X_(red)=X_(ox) such that X_(red)/X_(ox)=1, the half-cellis at 50% SOC, and the half-cell potential equals the standard Nemstianvalue, E⁰. When the concentration ratio at the electrode surfacecorresponds to X_(red)/X_(ox)=0.25 or X_(red)/X_(ox)=0.75, the half-cellis at 25% and 75% SOC respectively. The SOC for a full cell depends onthe SOCs of the individual half-cells and in certain embodiments the SOCis the same for both positive and negative electrodes.

EXAMPLES

The following Examples are provided to illustrate some of the conceptsdescribed within this disclosure. While each Example is considered toprovide specific individual embodiments of composition, methods ofpreparation and use, none of the Examples should be considered to limitthe more general embodiments described herein.

Example 1

Three samples of the redox couple iron(III) hexacyanide/iron(II)hexacyanide were prepared with three distinct ratios of the oxidized(Fe³⁺) to reduced (Fe³⁺) species. The samples were prepared by thedissolution of the potassium salts K₄Fe^(III)(CN)₆ and K₃Fe^(II)(CN)₆ inthe appropriate molar ratios 20% Fe³⁺/80% Fe²⁺, 60% Fe³⁺/40% Fe²⁺, and95% Fe³⁺/5% Fe²⁺. The total concentration of iron in each sample was 1.0M. In this case the state of charge (SOC) of each solution is defined tobe the percentage of the Fe³⁺ species.

A 0.3 cm diameter glassy carbon disc working electrode (BioanalyticalSystems, Inc.), with a surface area of 0.071 cm², and a 0.4 cm glassycarbon rod (Alfa Aesar) with a surface area of approximately 5 cm² wereplaced into contact with each solution and connected to a potentiostat.The glassy carbon rod was connected as both the counter and referenceelectrode.

For each sample, the potential of the working electrode was set to +0.1V and held for 300 s while recording the current (I_(lim,ox)).Subsequently the potential was set to −0.1 V and held for 300 s whilerecording the current (I_(lim, red)). Measurements were taken withoutstirring of the solutions. The resulting currents are plotted in FIGS.3, 4, and 5. The current at 300 s was taken to be the constant currentfor each hold. The oscillation present in the current for the negativepotential holds is attributed to a limitation of the potentiostat, andnot inherent to limiting current behavior at the electrode or in theelectrolyte. The measured constant currents, ratio of the currents, andthe resulting SOC (or % Fe³⁺) are listed in Table 1. The SOC wascalculated using:

${SOC} = {100\; \frac{A\frac{\; I_{\lim,{red}}}{I_{\lim,{ox}}}}{1 + {A\; \frac{I_{\lim,{red}}}{I_{\lim,{ox}}}}}}$

with the the coefficient A equal to 1.

TABLE 1 Currents and SOC for Fe³⁺/Fe²⁺ Samples Calculated (as prepared)Experimental SOC SOC (% Fe³⁺) I_(red)/I_(ox) I_(lim, ox) I_(lim, red)I_(red)/I_(ox) (% Fe³⁺) 20 0.25 −0.21 mA 0.08 mA 0.38 27 60 1.5 −0.16 mA0.32 mA 2.0 67 95 19 −0.02 mA 0.27 mA 14 93

Example 2

Four additional samples of the redox couple iron(III)hexacyanide/iron(II) hexacyanide were prepared as described in Example1, with molar ratios 36.0% Fe³⁺/64.0% Fe²⁺, 53.4% Fe³⁺/46.6% Fe²⁺, 76.8%Fe³⁺/23.2% Fe²⁺, and 100% Fe³⁺/0.00% Fe²⁺. The total concentration ofiron in each sample was 0.92 M. Again, the state of charge (SOC) of eachsolution is defined to be the percentage of the Fe³⁺ species.

A 0.3 cm diameter glassy carbon disc working electrode (BioanalyticalSystems, Inc.), with a surface area of 0.071 cm², and a 0.4 cm glassycarbon rod (Alfa Aesar) with a surface area of approximately 5 cm² wereplaced into contact with each solution and connected to a potentiostat.The glassy carbon rod was connected as both the counter and referenceelectrode.

In these cases, the potential of the working electrode was set to +0.2 Vand held for over 60 seconds while recording the current (I_(lim,ox)).Subsequently the potential was set to −0.2 V and held for over 60seconds while recording the current (I_(lim, red)). Measurements weretaken without stirring of the solutions. The resulting currents areplotted in FIGS. 6, 7, 8, and 9. The current at 60 s was taken to be theconstant current for each hold. The measured constant currents, ratio ofthe currents, and the resulting SOC (or % Fe³⁺ are listed in Table 2.The SOC was calculated using:

${SOC} = {100\; \frac{A\; \frac{I_{\lim,{red}}}{I_{\lim,{ox}}}}{1 + {A\; \frac{I_{\lim,{red}}}{I_{\lim,{ox}}}}}}$

with the coefficient A taken to be 1.

TABLE 2 Limiting Currents and SOC for Fe³⁺/Fe²⁺ Samples - Example 2Calculated (as prepared) Experimental SOC SOC (% Fe³⁺) I_(lim, ox)I_(lim, red) I_(red)/I_(ox) (% Fe³⁺) 36.0  −1.11 mA 0.548 mA 0.49 33.153.4 −0.791 mA 0.842 mA 1.06 51.6 76.8 −0.318 mA  1.23 mA 3.87 79.5 100−0.00276  1.54 mA 556 99.8

As those skilled in the art will appreciate, numerous modifications andvariations of the present invention are possible in light of theseteachings, and all such are contemplated hereby. For example, inaddition to the embodiments described herein, the present inventioncontemplates and claims those inventions resulting from the combinationof features of the invention cited herein and those of the cited priorart references which complement the features of the present invention.Similarly, it will be appreciated that any described material, feature,or article may be used in combination with any other material, feature,or article, and such combinations are considered within the scope ofthis invention.

The disclosures of each patent, patent application, and publicationcited or described in this document are hereby incorporated herein byreference, each in its entirety, for all purposes.

What is claimed:
 1. A method of determining the ratio of the oxidizedand reduced forms of a redox couple in solution, said method comprising:(a) contacting a first stationary working electrode and a first counterelectrode to the solution; (b) contacting a second stationary workingelectrode and a second counter electrode to the solution; (c) applying afirst potential at the first stationary working electrode relative tothe first counter electrode and measuring a first constant current forthe first stationary working electrode; and (d) applying a secondpotential at the second stationary working electrode relative to thesecond counter electrode and measuring a second constant current for thesecond stationary working electrode; wherein the first and secondconstant currents have opposite signs; and wherein the ratio of theabsolute values of the first and second constant currents reflects theratio of the oxidized and reduced forms of the redox couple in solution.2. The method of claim 1, wherein the first and second potentials areapplied simultaneously.
 3. The method of claim 1, wherein the first andsecond potentials are of substantially the same magnitude but oppositein sign.
 4. The method of claim 1, wherein the first and secondstationary working electrodes and the first and second counterelectrodes each have a surface area contacting the solution, and each ofthe first and second stationary working electrode surface areas is lessthan that of the first and second counter electrodes.
 5. The method ofclaim 4, wherein the surface areas of the first and second stationaryworking electrodes are each less than about 20% of the surface areas ofthe first and second counter electrodes, respectively.
 6. The method ofclaim 1, wherein the first and second stationary working electrodes andthe first and second counter electrodes each have a surface areacontacting the solution, and each surface area of the first and secondstationary working electrodes is substantially the same.
 7. The methodof claim 1, wherein the ratio of the oxidized and reduced forms of theredox couple are in a range of from about 5:95 to 95:5.
 8. The method ofclaim 1, wherein the ratio of the oxidized and reduced forms of theredox couple are in a range of from about 20:80 to 80:20.
 9. The methodof claim 1, wherein the redox couple comprises a metal or metalloid ofGroups 2-16, including the lanthanide and actinide elements, or acoordination compound thereof.
 10. The method of claim 1, wherein theredox couple is a reversible redox couple.
 11. The method of claim 1,wherein the redox couple is a quasi-reversible redox couple.
 12. Themethod of claim 1, wherein the solution is an aqueous solution.
 13. Themethod of claim 1, wherein the solution is a non-aqueous solution. 14.The method of claim 1, wherein the solution is moving.
 15. The method ofclaim 1, wherein at least one of the stationary working electrodes or atleast one of the counter electrodes comprises an allotrope of carbon.16. The method of claim 1, wherein a constancy of at least one of thefirst or second constant currents is characterized by a change of lessthan 0.1% over one second or less than 1% over ten seconds.
 17. Themethod of claim 1, wherein the solution is contained within a half-cellfluidic loop of an operating flow battery cell or other operatingelectrochemical cell, said operating electrochemical cell generating orstoring electrical energy.
 18. The method of claim 1, wherein the ratioof oxidized and reduced forms of the redox couple in solution based onthe ratio of the absolute values of the first and second constantcurrents is determined by applying an experimentally derived correctionfactor.
 19. A method of maintaining an electrochemical cell, said cellhaving at least one half-cell comprising oxidized and reduced forms of aredox couple in solution, said method comprising: determining the theratio of the oxidized and reduced forms of a redox couple in solutionaccording to claim 1; and (e) oxidizing or reducing the solution, so asto alter a balance of the oxidized and reduced forms of the redox couplein solution, to a degree dependent on the ratio of the absolute valuesof the first and second constant currents.
 20. The method of claim 19,wherein the first and second potentials are applied simultaneously. 21.The method of claim 19, wherein the first and second potentials are ofsubstantially the same magnitude but opposite in sign.
 22. The method ofclaim 19, wherein the first and second stationary working electrodes andthe first and second counter electrodes each have a surface areacontacting the solution, and each of the first and second stationaryworking electrode surface areas is less than that of the first andsecond counter electrodes.
 23. The method of claim 21, wherein thesurface areas of the first and second stationary working electrodes areeach less than about 20% of the surface areas of the first and secondcounter electrodes, respectively.
 24. The method of claim 19, whereinthe first and second stationary working electrodes and the first andsecond counter electrodes each have a surface area contacting thesolution, and each surface area of the first and second stationaryworking electrodes is substantially the same.
 25. The method of claim19, wherein the ratio of the oxidized and reduced forms of the redoxcouple are in a range of from about 5:95 to 95:5.
 26. The method ofclaim 19, wherein the ratio of the oxidized and reduced forms of theredox couple are in a range of from about 20:80 to 80:20.
 27. The methodof claim 19, wherein the redox couple comprises a metal or metalloid ofGroups 2-16, including the lanthanide and actinide elements, or acoordination compound thereof.
 28. The method of claim 19, wherein theredox couple is a reversible redox couple.
 29. The method of claim 19,wherein the redox couple is a quasi-reversible redox couple.
 30. Themethod of claim 19, wherein the solution is an aqueous solution.
 31. Themethod of claim 19, wherein the solution is a non-aqueous solution. 32.The method of claim 19, wherein the solution is moving.
 33. The methodof claim 19, wherein at least one of the stationary working electrodesor at least one of the counter electrodes comprises an allotrope ofcarbon.
 34. The method of claim 19, wherein a constancy of at least oneof the first or second constant currents is characterized by a change ofless than 0.1% over one second or less than 1% over ten seconds.
 35. Themethod of claim 19, wherein the solution is contained within a half-cellfluidic loop of an operating flow battery cell or other operatingelectrochemical cell, said operating electrochemical cell generating orstoring electrical energy.
 36. The method of claim 19, wherein oxidizingor reducing the solution is performed electrochemically.
 37. The methodof claim 36, wherein oxidizing or reducing the solution takes place in arebalancing sub-system within a half-cell fluidic loop of anelectrochemical cell.
 38. The method of claim 19, wherein the ratio ofoxidized and reduced forms of the redox couple in solution based on theratio of the absolute values of the first and second constant currentsis determined by applying an experimentally derived correction factor.39. A device comprising: at least one pair of electrodes independentlyin fluidic contact with an electrolyte solution, each pair of electrodesconsisting of a first stationary working electrode and a first counterelectrode; a control system, including a power source and sensors,associated with each pair of electrodes, said control system configuredto be capable of applying first and second electric potentials at eachof the first working electrodes relative to the first counterelectrodes, and measuring first and second currents associated with saidfirst and second electric potentials; and software capable ofcalculating the ratio of the absolute values of the first and secondcurrents between each electrode pair, which reflects the ratio of theoxidized and reduced forms of a redox couple in solution; and the deviceused in the implementation of the method of claim
 1. 40. A devicecomprising: at least one pair of electrodes independently in fluidiccontact with an electrolyte solution, each pair of electrodes consistingof a first stationary working electrode and a first counter electrode; acontrol system, including a power source and sensors, associated witheach pair of electrodes, said control system configured to be capable ofapplying first and second electric potentials at each of the firstworking electrodes relative to the first counter electrodes, andmeasuring first and second currents associated with said first andsecond electric potentials; and software capable of calculating theratio of the absolute values of the first and second currents betweeneach electrode pair, which reflects the ratio of the oxidized andreduced forms of a redox couple in solution; and the device used in theimplementation of the method of claim 19.